Suits in black, navy blue, charcoal grey, or even a white/cream color would go well with this black and gold checkered pocket square.    
Black Suit: A black suit provides a classic, formal, and high-contrast backdrop, allowing the gold in the pocket square to stand out prominently.  
Navy Blue Suit: Navy is a versatile, dark neutral that offers a sophisticated contrast. The gold accents in the pocket square can complement the deep blue tone well.  
Charcoal or Dark Grey Suit: Similar to navy, a dark grey suit is a strong, neutral base that pairs effectively with both black and gold, creating a balanced and sharp look.  
White or Cream Suit/Blazer: For a more striking, high-fashion, or warm-weather look, a white or cream suit would offer a bright contrast that makes the pocket square a focal point. 
When pairing, ensure that the suit and pocket square have different patterns or textures to avoid a matching look, which is generally less stylish than a coordinated one. The key is to have sufficient contrast so the pocket square is a clear accessory and not lost in the outfit.